Extend the geometric reformulation to PC-SAFT regression

Develop and validate an actual PC-SAFT parameter regression using the geometric bilevel reformulation, thereby extending the demonstrated applications beyond NRTL and Peng–Robinson models.

Background

The paper presents the dual-manifold formulation as model-agnostic and states that it can accommodate non-cubic equations of state, including PC-SAFT. However, the reported fitting results cover binary NRTL systems and Peng–Robinson or Soave–Redlich–Kwong validation cases, while PC-SAFT is only implemented as an adapter and is not subjected to an actual regression study.

A concrete unresolved extension is therefore to carry the geometric formulation through a complete PC-SAFT parameter-estimation problem and establish its performance and stability guarantees in that setting.

References

Carrying that argument through to an actual PC-SAFT regression is left to future work.

— A geometric reformulation of the bilevel parameter optimization problem to a single level non-linear programming problem with applications to phase equilibria  (2608.17806 - Endres et al., 18 Aug 2026) in Section Conclusions, paragraph beginning “The construction is also model-agnostic by design”